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Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules

Authors
Boscarino, SebastianoCho, Seung YeonRusso, GiovanniYun, Seok-Bae
Issue Date
Apr-2022
Publisher
EDP SCIENCES S A
Keywords
Polyatomic ellipsoidal BGK model; Boltzmann equation; semi-Lagrangian scheme; error estimate; kinetic theory of gases
Citation
Esaim-mathematical Modelling and Numerical Analysis, v.56, no.3, pp 893 - 942
Pages
50
Indexed
SCIE
Journal Title
Esaim-mathematical Modelling and Numerical Analysis
Volume
56
Number
3
Start Page
893
End Page
942
URI
https://scholarworks.gnu.ac.kr/handle/sw.gnu/1372
DOI
10.1051/m2an/2022022
ISSN
2822-7840
Abstract
In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the convection term with an implicit treatment for the relaxation term. We show how to explicitly solve the implicit step, thus obtaining an efficient and stable scheme for any Knudsen number. We also derive an explicit error estimate on the convergence of the proposed scheme for every fixed value of the Knudsen number.
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